Study on the Nonlinear Dynamics of a Single-Stage Gear Vibro-Impact System

2014 ◽  
Vol 697 ◽  
pp. 161-167 ◽  
Author(s):  
Ruo Yu Sheng ◽  
Yong Wang ◽  
Li Na Zhang
Keyword(s):  
Dynamic Model ◽  
Periodic Motion ◽  
Linear Time ◽  
Gear Tooth ◽  
Equations Of Motion ◽  
Simulation Method ◽  
Spur Gear ◽  
Single Stage ◽  
Gear Train ◽  
Linear Time Invariant

A vibro-impact dynamic model of a typical single-stage spur gear train has been proposed in this study. The lumped parameter dynamic model includes the constant meshing stiffnesses, the linear time-invariant viscous damping values and the gear clearance (backlash) non-linearity allowing teeth separations. With taking account of the effect on impact of gear tooth when meshing, the dynamic equations of motion are solved for the steady period response by use of analytical method under given periodic motion conditions. The feasibility of the given periodic motion conditions is demonstrated by comparing the analytical results with that of numeric simulation method. A Poincaré map of the system is established. The stability and bifurcation of the system are studied using analytical methods. Finally, the theoretical analyses are verified using numerical simulation.

Planetary Gear Train Dynamics

1994 ◽  
Vol 116 (3) ◽  
pp. 713-720 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Dynamic Behavior ◽  
Linear Time ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Planetary Gear ◽  
Gear Train ◽  
Planetary Gear Train ◽  
Gear Teeth ◽  
Linear Time Invariant ◽  
Mesh Phasing

A model to simulate the dynamic behavior of a single-stage planetary gear train with helical gears is developed. The three-dimensional dynamic model includes all six rigid body motions of the gears and the carrier. The generic nature of the formulation allows the analysis of a planetary gear set with any number of planets. Planets can be arbitrarily spaced (equally or unequally) around the sun gear. The model is also capable of handling different planet meshing conditions which are functions of number of gear teeth and planet positions. The linear time-invariant equations of motion are solved to obtain the natural modes and the forced vibration response due to static transmission errors. The proposed model is employed to describe the effects of the planet mesh phasing conditions on the dynamic behavior of a four-planet system.

Accurate Model for the Minimum Volume Design of Single Stage Spur Gear Train

2015 ◽  
Author(s):  
Cheng Wang ◽  
Zhao Yao Shi
Keyword(s):  
Structural Changes ◽  
Spur Gear ◽  
Single Stage ◽  
Type Structure ◽  
Gear Train ◽  
Volume Calculation ◽  
Existing Problems ◽  
Design Variables ◽  
Fixed Structure ◽  
Volume Models

At present, the existing problems in gear volume optimization include: (1) the clearance volume caused by the bottom clearance and addendum modification is not considered in the volume models which causes the error of volume calculation. (2) Gears employ fixed structure and their structural changes caused by the dimension changes are not considered in the process of optimization. In view of the above mentioned problems, the paper firstly deduces the formula of clearance volume. An example is provided to verify that the clearance volume should be considered in the accurate calculation of gear volume. Secondly, volume formulas of different structure of spur gear including solid structure, web-type structure, spoke type structure with cross shape section and with H-shape section are deduced. The design variables, objective function and constrains are briefly introduced. Finally, a single stage spur gear train is as an example, the optimization is carried out. The result shows when the transmission ratio is changed from 3.2 to 2, the structure of gear changes from the web-type to the solid. It means gear with fixed structure is not reasonable in the process of optimization.

Strength Evaluation of Polymer Composite Spur Gear by Finite Element Analysis

2008 ◽  
Author(s):  
Mohammad Robiul Hossan ◽  
Zhong Hu
Keyword(s):  
Finite Element ◽  
Polymer Composite ◽  
Volume Fraction ◽  
Gear Tooth ◽  
Axial Stress ◽  
High Stress ◽  
Element Model ◽  
Simulation Method ◽  
Spur Gear ◽  
Element Analysis

Modern advanced polymer composite materials have opened a new level of noiseless, lubricant free, high resilience and precision gearing in power and motion transmission. The proper understanding and evaluation of gear strength and performance is an important prerequisite for any reliable application. In this paper, a 20% short glass fiber reinforced nylon66 spur gear fabricated by injection molding has been carefully investigated. A three-dimensional finite element model was used to simulate the multi-axial stress-strain behaviors of a gear tooth under the dynamic load for a complete working cycle with a special geometry, operating condition, fiber orientation and volume fraction. The strength of composite gears has been compared with isotropic un-reinforced nylon66 and steel gears. The tooth root region of a gear which usually experiences high stress and potential to failure has been carefully investigated. This computer simulation method can be used as a useful tool for evaluating strength and predicting failure of the polymer composite gears.

scholarly journals Fault Feature Analysis of Gear Tooth Spalling Based on Dynamic Simulation and Experiments

Materials ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6053
Author(s):  
Zhiguo Wan ◽  
Jie Zheng ◽  
Jie Li ◽  
Zhenfeng Man
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Gear Tooth ◽  
Resonance Region ◽  
Spur Gear ◽  
Gear System ◽  
Parameter Method ◽  
Coupling Vibration ◽  
Shock Response ◽  
Potential Energy Method

Gear dynamics analysis based on time-varying meshing stiffness (TMS) is an important means to understand the gear fault mechanism. Based on Jones bearing theory, a bearing statics model was established and introduced into a gear system. The lateral–torsion coupling vibration model of the gear shaft was built by using a Timoshenko beam element. The lumped parameter method was used to build the dynamic model of a gear pair. The dynamic model of a spur gear system was formed by integrating the component model mentioned above. The influence of rectangular and elliptical spalling on TMS was analyzed by the potential energy method (PEM). The fault feature of tooth spalling was studied by dynamic simulation and verified by experiments. It is found that the gear system will produce a periodic shock response owing to the periodic change of the number of meshing gear teeth. Due to the contact loss and the decrease of TMS, a stronger shock response will be generated when the spalling area is engaged. In the spectrum, some sidebands will appear in the resonance region. The results can provide a theoretical guide for the health monitoring and diagnosis of gear systems.

scholarly journals Dynamic Tooth Loads and Stressing for High Contact Ratio Spur Gears

1978 ◽  
Vol 100 (1) ◽  
pp. 69-76 ◽  
Author(s):  
R. W. Cornell ◽  
W. W. Westervelt
Keyword(s):  
Dynamic Model ◽  
Gear Tooth ◽  
Closed Form Solution ◽  
Time History ◽  
Spur Gear ◽  
Form Solution ◽  
Tooth Profile ◽  
Contact Ratio ◽  
Modification System ◽  
Work Done

A time history, closed form solution is presented for a dynamic model of spur gear systems for all practical contact ratios. The analysis determines the dynamic response of the gear system and the associated tooth loads and stressing. The dynamic model is based on work done by Richardson and Howland [2, 3], and assumes the two gears act as a rigid inertia and the teeth act as a variable spring of a dynamic system excited by the meshing action of the teeth. Included in the analysis are the effects of the non-linearity of the tooth pair stiffness during mesh, the tooth errors, and the tooth profile modifications. Besides reviewing the features, solution, and program of this analysis, preliminary results from applying the analysis are presented, which show that tooth profile modification, system inertia and damping, and system critical speeds can affect the dynamic gear tooth loads and stressing significantly.

Non-linear dynamic behaviour of compound planetary gear trains: Model formulation and semi-analytical solution

2009 ◽  
Vol 223 (3) ◽  
pp. 199-210 ◽  
Author(s):  
A Al-Shyyab ◽  
K Alwidyan ◽  
A Jawarneh ◽  
H Tlilan
Keyword(s):  
Power Flow ◽  
Linear Time ◽  
Equations Of Motion ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Periodic Variation ◽  
Gear Train ◽  
Gear Mesh ◽  
Non Linear ◽  
Direct Numerical Integration

A discrete, non-linear, time-varying, torsional dynamic model of a multi-stage planetary train that is formed by any number of simple planetary stages is proposed in this study. Each planetary stage has a distinct fundamental mesh frequency and any number of planets spaced in any angular positions. The model allows the analysis of the gear train in all possible power flow configurations suitable for various gear drive ratios. It includes periodic variation of gear mesh stiffnesses as well as clearance (backlash) non-linearities that allow tooth separations. Equations of motion for the general case are formulated and solved semi-analytically using a hybrid harmonic balance method (HBM) in conjugate with inverse Fourier transform. Relative mesh displacements along lines of action of individual gear pairs were used as the continuation parameters to pass singular points and ill-conditioned equations in their proximity. At the end, a case study of a two-stage planetary train is used to demonstrate the effectiveness of the model and solution methods. The HBM solutions are compared to those obtained by a direct numerical integration method to assess their accuracy.

Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

2003 ◽  
Vol 126 (3) ◽  
pp. 534-541 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dogˇruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Degree Of Freedom ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Gear Mesh

This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine multi harmonic responses of nonlinear multi-degree-of-freedom systems is employed for the solution. The excitations considered in the model are external static torque and internal excitation caused by mesh stiffness variation, gear errors and gear tooth profile modifications. The model suggested and the solution method presented combine the versatility of modeling a shaft-bearing-disk system that can have any configuration without a limitation to the total degree of freedom, with the accuracy of a nonlinear gear mesh interface model that allows to predict jumps and double solutions in frequency response. Thus any single stage gear mesh configuration can be modeled easily and accurately. With the model developed it is possible to calculate dynamic gear loads, dynamic bearing forces, dynamic transmission error and bearing displacements. Theoretical results obtained by using the method suggested are compared with the experimental data available in literature, as well as with the theoretical values calculated by employing a previously developed nonlinear single degree of freedom model.

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